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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 393008u
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 393008.u1 | 393008u1 | \([0, -1, 0, -122613, 24942205]\) | \(-28094464000/20657483\) | \(-149897180122984448\) | \([]\) | \(2903040\) | \(1.9952\) | \(\Gamma_0(N)\)-optimal |
| 393008.u2 | 393008u2 | \([0, -1, 0, 1000267, -384684419]\) | \(15252992000000/17621717267\) | \(-127868711171046551552\) | \([]\) | \(8709120\) | \(2.5445\) |
Rank
sage: E.rank()
The elliptic curves in class 393008u have rank \(0\).
Complex multiplication
The elliptic curves in class 393008u do not have complex multiplication.Modular form 393008.2.a.u
sage: E.q_eigenform(10)
Isogeny matrix
sage: E.isogeny_class().matrix()
The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the Cremona numbering.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
